Non-Gaussian operations, which map Gaussian states into non-Gaussian states, are a common approach to delivering non-Gaussian features into a quantum system.
At the core of non-Gaussian operations is the application of the annihilation operator \({A}\)  and the creation operator \({A}^\dagger \) .
There are two basic types of these operations, namely photon subtraction (PS) and photon addition (PA), which apply \({A}\)  and \({A}^\dagger \)  to a state, respectively.
Both operations have been shown to enhance the entanglement of TMSV states (e.g., [1]}, [2]}, [3]}).
Various studies on combinations of PS and PA have also been undertaken (e.g., [4]}, [5]}, [6]}, [7]}).
A specific combination, photon catalysis (PC), is of particular research interest.
Instead of subtracting or adding photons, PC replaces photons from a state, and is known to significantly enhance the entanglement of TMSV states under certain conditions (e.g., [8]}, [9]}).
If TMSV states are in fact shared between a satellite and a ground station, it is natural to ask whether non-Gaussian operations can be adopted at the ground station to further facilitate satellite-based quantum teleportation.
